Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-9x+7y &= -4 \\ 5x-5y &= 6\end{align*}$
Answer: Begin by moving the $y$ -term in the second equation to the right side of the equation. $5x = 5y+6$ Divide both sides by $5$ to isolate $x$ $x = {y + \dfrac{6}{5}}$ Substitute this expression for $x$ in the first equation. $-9({y + \dfrac{6}{5}}) + 7y = -4$ $-9y - \dfrac{54}{5} + 7y = -4$ Simplify by combining terms, then solve for $y$ $-2y - \dfrac{54}{5} = -4$ $-2y = \dfrac{34}{5}$ $y = -\dfrac{17}{5}$ Substitute $-\dfrac{17}{5}$ for $y$ in the top equation. $-9x+7( -\dfrac{17}{5}) = -4$ $-9x-\dfrac{119}{5} = -4$ $-9x = \dfrac{99}{5}$ $x = -\dfrac{11}{5}$ The solution is $\enspace x = -\dfrac{11}{5}, \enspace y = -\dfrac{17}{5}$.